Answer :

First, let's expand the expression and reduce like terms:

[tex]\begin{gathered} (x-5)^2-4=0 \\ \rightarrow x^2-10x+25-4=0 \\ \rightarrow x^2-10x+21=0 \end{gathered}[/tex]

Now, let's factor the new expression completely:

[tex](x-3)(x-7)=0[/tex]

Thereby, the correct answer is option C

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